Question

prove the curve x=y^2 and xy=kcut at right angle triangle ??​

Answer 1

Step-by-step explanation:

x=y2;xy=k

Let the curves cut each other at (a,b)

a=b2;ab=k

x=y2;xy=k

1=2ydxdy;xdxdy+y=0

dxdy=21y;dxdy=x−y

Slope at a,b=2b1; Slope at a,b=a−b

m1=2b1;m2=a−b

If the curves cut at right angles

m1m2=−1

2b1a−b=−1

2a=1→1

a=b2;ab=k

b2.b=k

b3/2=k

b=k2/3

Substituting in eq. 1

2.b2=1

2.k2/3=1

∴8k2=1